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- Roman Chapko
- 2007

We consider the inverse problem to determine the shape of an insulated inclusion within a heat conducting medium from overdetermined Cauchy data of solutions for the heat equation on the accessible exterior boundary of the medium. For the approximate solution of this ill-posed and nonlinear problem we propose a regularized Newton iteration scheme based on a… (More)

- Roman Chapko
- 1999

We consider the initial boundary value problem for the heat equation in a region with in nite and nite boundaries (direct problem) and the related problem to reconstruct the nite boundary from Cauchy data on the in nite boundary (inverse problem). The numerical solution of the direct problem is realized by a boundary integral equation method. For an… (More)

- Roman Chapko, B. Tomas Johansson, V. Vavrychuk
- Mathematics and Computers in Simulation
- 2014

- Roman Chapko
- Mathematics and Computers in Simulation
- 2004

- Roman Chapko
- Applied Mathematics and Computation
- 2004

- Roman Chapko, B. Tomas Johansson, Olena Protsyuk
- Int. J. Comput. Math.
- 2012

A direct boundary integral equation method for the numerical construction of harmonic functions in threedimensional layered domains containing a cavity Roman Chapko a , B. Tomas Johansson b & Olena Protsyuk a a Faculty of Applied Mathematics and Informatics , Ivan Franko National University of Lviv , 79000 , Lviv , Ukraine b School of Mathematics ,… (More)

- Roman Chapko
- 2016 IEEE International Conference on…
- 2016

We consider two types of inverse boundary problems related to the Laplace equation in planar double connected domains. The first one consists in the determining the Cauchy data on an inclusion from given Cauchy data on an accessible exterior boundary. On this accessible part the function (or the normal derivative) is known and, additionally, on a portion of… (More)

- Roman Chapko, Christina Babenko, Volodymyr Khlobystov, Volodymyr L. Makarov
- Int. J. Comput. Math.
- 2014

On the interpolation of a function on a bounded domain by its traces on parametric hypersurfaces Roman Chapko, Christina Babenko, Volodymyr Khlobystov & Volodymyr Makarov a Faculty of Applied Mathematics and Informatics, Ivan Franko National University of Lviv, Lviv, Ukraine b Ukrainian Engineering Pedagogics Academy, Kharkiv, Ukraine c Institute of… (More)

- Roman Chapko, Rainer Kressy
- 2007

In this paper we describe a fully discrete quadrature method for the numerical solution of a hypersingular integral equation of the rst kind for the scattering of time-harmonic elastic waves by a cavity crack. We establish convergence of the method and prove error estimates in a HH older space setting. Numerical examples illustrate the convergence results.

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